Diagram

[dshier89]

Can someone help me with this one? I honestly had no idea how to attack this.

[timmydoeslsat]

This game tells us that we have 6 cars. 2 are to be green, 2 are to be orange, and 2 are to be purple. I like to list items like this as follows: GG, OO, PP

Our constraints tell us that no car can be next to another car of the same color. I did not denote this rule in my base diagram, as I simply internalized it in my head. You could write out: ~GG, ~OO, ~PP to indicate that they could not occupy consecutive spaces.

The rules tell us that either Car 5 or Car 6 must be purple. A minor inference in this rule is that only one of Car 5 and 6 can be purple, as if both were purple, then that would violate the consecutive color rule.

The next rule says that Car 1 cannot be O, so we know Car 1 is either G or P

The following rule says that car 4 cannot be G, so we know it is either O or P.

The things I would advise you to do before you attack the questions is to look at the game as a whole.

Could you have Car 1 and 4 both be purple? No! Because then there would not be a purple available to occupy one of the 5 or 6 car slots.

Also notice what happens if Car 1 is purple or Car 4 is purple. Whichever one is purple forces the other car to be the other color. For example, if Car 4 is purple, then Car 1 cannot be purple, so it must be green. That also means that since Car 4 is purple, that car 5 cannot be purple since it would be next to another purple, thus car 6 must be purple.

Let me know if you need any help when you rework this game!

[giladedelman]

Great explanation, and I love the DIY diagram!